Geodesic
Some remarks on the complement of the Armendariz graph of a commutative ring
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 5-24

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Let R be a commutative ring with identity which is not an integral domain. Let Z(R) denote the set of all zero-divisors of R. Recall from that the Armendariz graph of R denoted by A(R) is an undirected graph whose vertex set is Z(R[X])\{0} and distinct vertices f(X) = ∑_i = 0^na_iX^i and g(X) = ∑_j = 0^mb_jX^j are adjacent in A(R) if and only if a_ib_j = 0 for all i∈{0, …, n} and j∈{0, …, m}. The aim of this article is to study the interplay between the graph-theoretic properties of the complement of A(R), that is, (A(R))^c and the ring-theoretic properties of R.
Keywords: B-prime of $(0)$, complement of the zero-divisor graph, diameter, domination number, maximal N-prime of $(0)$, radius 
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Visweswaran, Subramanian; Patel, Hiren D. Some remarks on the complement of the Armendariz graph of a commutative ring. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 1, pp. 5-24. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_1_a0/